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   "source": [
    "# Homework Set 9"
   ]
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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
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    "%pylab inline"
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   "source": [
    "## Problem 1\n",
    "\n",
    "\n",
    "Similar to our example in class, here is the table of future liabilities (in $millions):\n",
    "\n",
    "|  Years | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |\n",
    "| :-----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: |\n",
    "|  Benefits($millions) | 24 | 26 | 28 | 28 | 26 | 29 | 32 | 33 | 34 |\n",
    "\n",
    "\n",
    "And here is the set of bonds that can be invested in:\n",
    "\n",
    "|  Bonds | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |\n",
    "| :-----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: |\n",
    "|  Price | 102 | 101.625 | 103 | 102 | 102 | 103 | 101 | 101.5 | 102 | 102.75 | 103 | 104 |\n",
    "|  Coupon(%) | 1.25 | 1.5 | 2.5 | 1.75 | 2.125 | 2.5 | 2.625 | 3 | 3.125 | 3.5 |  3.75 | 4.5 |\n",
    "|  Maturity(Years) | 1 | 2 | 2 | 3 | 4 | 5 | 5 | 6 | 7 | 8 |  8 | 9 |\n",
    "\n",
    "\n",
    "Consider two excess cash scenarios: 1) not reused at each period. 2) reinvested at 1% interest rate and reused. \n",
    "Find the **least cost** portfolio of bonds so that the pension fund can meet its future liabilities. Please show your LP problem set up.\n"
   ]
  }
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